187edt
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Prime factorization
11 × 17
Step size
10.1709¢
Octave
118\187edt (1200.16¢)
Consistency limit
11
Distinct consistency limit
11
 |
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187 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 187edt or 187ed3), is a nonoctave tuning system that divides the interval of 3/1 into 187 equal parts of about 10.2 ¢ each. Each step represents a frequency ratio of 31/187, or the 187th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.16 | +0.00 | +0.33 | +0.51 | +0.16 | -2.26 | +0.49 | +0.00 | +0.67 | -1.60 | +0.33 |
| Relative (%) | +1.6 | +0.0 | +3.2 | +5.0 | +1.6 | -22.3 | +4.8 | +0.0 | +6.6 | -15.7 | +3.2 | |
| Steps (reduced) |
118 (118) |
187 (0) |
236 (49) |
274 (87) |
305 (118) |
331 (144) |
354 (167) |
374 (0) |
392 (18) |
408 (34) |
423 (49) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.15 | -2.10 | +0.51 | +0.66 | -2.59 | +0.16 | -1.90 | +0.84 | -2.26 | -1.43 | +2.98 |
| Relative (%) | +40.8 | -20.6 | +5.0 | +6.5 | -25.5 | +1.6 | -18.7 | +8.2 | -22.3 | -14.1 | +29.3 | |
| Steps (reduced) |
437 (63) |
449 (75) |
461 (87) |
472 (98) |
482 (108) |
492 (118) |
501 (127) |
510 (136) |
518 (144) |
526 (152) |
534 (160) | |